2 full days should give you just enough time to check out the main attractions in George Town. Since George Town is very compact, everything is close to each other so you can actually see a lot of things in a day. You can spend the first day checking out the UNESCO Heritage Site (basically the entire old town), and eat at one of the many hawker centers at night. On day 2 you can see some of the surrounding areas like Penang Hill, Gurney Drive, Kek Lok Si
Beyond 2 days in George Town, the you can go to Batu Ferringhi in the north. This is a beach resort town where you can relax on the ocean. There's also a big national park close by you should check out. Or you can take a ferry to Butterworth on the mainland.
Of course all this can be rushed. You can easily spend more time in Penang if you take it slow. My friends sometimes take 1-2 week vacations to Penang to enjoy it slowly. They rent a scooter and ride around the entire island.